Obama has staked the credibility of the United States — and his presidency — on his call for a military operation to punish the Syrian government for its alleged use of chemical weapons against civilians last month.

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As of Sept. 4, lawmakers appear to be tentatively dividing into four camps over military action in Syria.

But the president faces hardening barriers in Congress, where both Republican critics and Democratic allies have voiced deep reservations or flat opposition to his proposal to intervene militarily in a predominantly Muslim nation after a decade of war overseas. Polls show that much of the American public is skeptical, too.

The urgency partly reflects the surprising way that Obama culminated days of deliberation over how to respond to President Bashar al-Assad’s alleged use of chemical weapons, which Obama called “an assault on human dignity” that cannot go unpunished. He announced Saturday that he would seek congressional approval for any military strike against the Syrian government, and he has struggled to rally support across party lines amid his previously scheduled trip to Sweden and Russia.

The White House lobbying effort has included direct conversations between Obama or top administration officials and at least 60 senators and at least 125 House members as of Thursday, according to a White House official, who spoke on the condition of anonymity to discuss internal administration operations.

Late Thursday afternoon, Vice President Biden and Antony Blinken, the deputy national security adviser, briefed a bipartisan group of House and Senate members in the White House Situation Room, an administration official said.

The outcome of a congressional vote, especially in the Republican­led House, is unclear, and the issue has blurred traditional party lines.

White House officials said they are not concerned about the vote trend in Congress so far. They said Obama, who is to return to Washington late Friday, will begin a more public campaign, including perhaps a presidential address, to win support from Congress and the American public for a strike.

The full Senate plans to begin considering as early as Friday a resolution authorizing the use of force after a divided Foreign Relations Committee this week backed limited military action. Majority Leader Harry M. Reid (D-Nev.) is “guardedly optimistic” that the resolution can pass, according to Senate aides.

But Sen. Joe Manchin III (W.Va.), a moderate Democrat who has been a bipartisan consensus-­builder, said Thursday that a military strike “would be the wrong course of action” before all diplomatic options are exhausted.

Here in St. Petersburg, Obama’s quandary over Syria — and his estrangement from the summit’s host and Syria’s key patron, Russian President Vladi­mir Putin — largely overshadowed the economic agenda of the Group of 20 meeting.

Obama used the gathering to privately press his G-20 colleagues to support a U.S.-led strike in words, if not resources. He found one possible ally in Japanese Prime Minister Shinzo Abe, who Obama said agrees that the Syrian attack should not go unpunished.

The White House detailed an extensive outreach to lawmakers that is being coordinated by aides in Washington, as well as by national security adviser Susan E. Rice and a key deputy, Benjamin J. Rhodes, who are traveling with Obama in Russia.

On Wednesday, Obama and senior White House officials made more than 25 phone calls to lawmakers from both parties. Chief of Staff Denis McDonough arranged calls with the Progressive Caucus and the Hispanic Caucus in the House, while Blinken held a conference call with Jewish House members.

The administration also has held classified briefings for any lawmaker who requests one detailing evidence that the alleged Aug. 21 chemical attack was carried out by Assad’s regime. The administration has said that more than 1,400 civilians, including at least 426 children, were killed when rockets containing highly toxic sarin gas were launched from regime territory and landed on rebel strongholds or contested areas in the Damascus suburbs.

Secretary of State John F. Kerry and Defense Secretary Chuck Hagel have participated in the Capitol Hill outreach. Samantha Power, the U.S. ambassador to the United Nations, said Thursday that the United States must “respond decisively to this horrific attack” in Syria.

Obama spent most of the day Thursday in private meetings with world leaders but spoke briefly with reporters at the start of one session. Seated at a long table across from Abe, Obama spoke about their “joint recognition that the use of chemical weapons in Syria is not only a tragedy but also a violation of international law that must be addressed.”

The loudest critic of military action in Syria is Putin, who has scoffed at U.S. allegations about the attack. Putin welcomed Obama to the ornate Constantine Palace, once the summer playground for Russian czars, with a formal handshake and about 15 seconds of chitchat. The two leaders do not plan to meet here, although U.S. officials said Obama and Putin may interact informally on the summit’s sidelines.

Obama has argued forcefully that a U.S.-led military strike is needed to enforce an international ban on the use of chemical weapons and to degrade the ability of Assad’s forces to use them again in a brutal conflict with rebels that is in its third year.

The State Department said Thursday that Kerry, who has been the administration’s most visible supporter of military action in Syria, will travel to Europe over the weekend for consultations with allies and partners. He is scheduled first to speak with European Union counterparts who are meeting in Lithuania. In Paris, Kerry will meet with senior French officials and with Arab League representatives.

In Washington, many lawmakers said they remain unconvinced that the United States should engage militarily in Syria, even after closed-door classified briefings led by national security officials.

“I’ve had more phone calls on this issue than on any issue I’ve ever had since I got here in 2001, and my phone calls, e-mails, faxes are running 96 percent no,” said Rep. John Abney Culberson (R-Tex.). He said that there’s “absolutely no question” that Assad attacked innocent civilians but that “America has absolutely no strategic interest involved, and we should stay out of it.”

A growing number of liberals also oppose military action, including key allies of House Minority Leader Nancy Pelosi (D-Calif.), who backs a strike. Rep. Niki Tsongas (D-Mass.), a member of the House Armed Services Committee, said, “I give the administration great credit for strongly making their case, but I still have many reservations about the unintended consequences of our actions.”

With a vote in the House several days away at least, aides said Pelosi has not started reaching out to individual lawmakers because she believes that colleagues need time to review hundreds of classified documents and other materials.

To help rally support for the authorization, Sen. Dianne Feinstein (D-Calif.) is asking the CIA to prepare DVDs for members of Congress containing video footage that supports the administration’s claims about the alleged chemical attack.

Feinstein, chairman of the Senate Select Committee on Intelligence, said Thursday that the video evidence will help inform lawmakers’ decisions.

Assad’s forces have used chemical weapons “between 11 and 14 times before” the Aug. 21 attack “but in small amounts,” Feinstein said. “And I looked at that as if they were testing it in some way. It is a very serious situation, and Assad’s got to understand there is a penalty for this.”

O’Keefe reported from Washington. Scott Wilson, Karen DeYoung, Greg Miller and Juliet Eilperin in Washington, Will Englund in St. Petersburg and Colum Lynch in New York contributed to this report.

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